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Home/Chain Registry/Block #1,370,035

Block #1,370,035

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/15/2015, 8:18:52 AM Β· Difficulty 10.8203 Β· 5,469,592 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
50e37297bf894994e53f84a0a9ab627b8b40ded0108b365e7369bdcf40730601
View on Chainz β†—

Difficulty

10.820347

Transactions

1

Size

200 B

Version

2

Bits

0ad20246

Nonce

1,798,248,297

Timestamp

12/15/2015, 8:18:52 AM

Confirmations

5,469,592

Merkle Root

69e94065d815d71ac1aaa4c61c9c0f207d2978ed9f58d0e7cf8ae09607cf71eb
Transactions (1)
Coinbase69e94065d815d7…8ae09607cf71eb
1 in β†’ 1 out8.5300 XPM109 B
AHCDdL91…Keyg5m1w
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.

3.182 Γ— 10⁹⁷(98-digit number)
31828548994263809027…22522338239339888640
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
3.182 Γ— 10⁹⁷(98-digit number)
31828548994263809027…22522338239339888639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.182 Γ— 10⁹⁷(98-digit number)
31828548994263809027…22522338239339888641
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
6.365 Γ— 10⁹⁷(98-digit number)
63657097988527618055…45044676478679777279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.365 Γ— 10⁹⁷(98-digit number)
63657097988527618055…45044676478679777281
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
1.273 Γ— 10⁹⁸(99-digit number)
12731419597705523611…90089352957359554559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.273 Γ— 10⁹⁸(99-digit number)
12731419597705523611…90089352957359554561
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
2.546 Γ— 10⁹⁸(99-digit number)
25462839195411047222…80178705914719109119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.546 Γ— 10⁹⁸(99-digit number)
25462839195411047222…80178705914719109121
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
5.092 Γ— 10⁹⁸(99-digit number)
50925678390822094444…60357411829438218239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.092 Γ— 10⁹⁸(99-digit number)
50925678390822094444…60357411829438218241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1370035

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 50e37297bf894994e53f84a0a9ab627b8b40ded0108b365e7369bdcf40730601

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 #1,370,035 on Chainz β†—
Circulating Supply:57,961,308 XPMΒ·at block #6,839,626 Β· updates every 60s
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