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Home/Chain Registry/Block #2,637,206

Block #2,637,206

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 8:40:07 PM Β· Difficulty 11.4269 Β· 4,196,701 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
3a86ce5bc2ad4fe3a1059ffe7e6dde2c310f4528587ab46670f478bb88e7e8a3
View on Chainz β†—

Difficulty

11.426870

Transactions

1

Size

200 B

Version

2

Bits

0b6d4762

Nonce

635,758,221

Timestamp

4/29/2018, 8:40:07 PM

Confirmations

4,196,701

Merkle Root

bc731d575e8fd02fbc42672c1a4afe44177cf47bdb9983ca68a68112ea8e0cc6
Transactions (1)
Coinbasebc731d575e8fd0…a68112ea8e0cc6
1 in β†’ 1 out7.6500 XPM109 B
AXsV2sYe…EUnFv3r5
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.546 Γ— 10⁹⁸(99-digit number)
15462602544351638819…62157408698305085440
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.546 Γ— 10⁹⁸(99-digit number)
15462602544351638819…62157408698305085439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.546 Γ— 10⁹⁸(99-digit number)
15462602544351638819…62157408698305085441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.092 Γ— 10⁹⁸(99-digit number)
30925205088703277639…24314817396610170879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.092 Γ— 10⁹⁸(99-digit number)
30925205088703277639…24314817396610170881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
6.185 Γ— 10⁹⁸(99-digit number)
61850410177406555278…48629634793220341759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.185 Γ— 10⁹⁸(99-digit number)
61850410177406555278…48629634793220341761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.237 Γ— 10⁹⁹(100-digit number)
12370082035481311055…97259269586440683519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.237 Γ— 10⁹⁹(100-digit number)
12370082035481311055…97259269586440683521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.474 Γ— 10⁹⁹(100-digit number)
24740164070962622111…94518539172881367039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.474 Γ— 10⁹⁹(100-digit number)
24740164070962622111…94518539172881367041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.948 Γ— 10⁹⁹(100-digit number)
49480328141925244222…89037078345762734079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2637206

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 3a86ce5bc2ad4fe3a1059ffe7e6dde2c310f4528587ab46670f478bb88e7e8a3

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,637,206 on Chainz β†—
Circulating Supply:57,915,480 XPMΒ·at block #6,833,906 Β· updates every 60s
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