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Block #617,919

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/5/2014, 9:08:48 AM Β· Difficulty 10.9466 Β· 6,208,668 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f7c557b81a0f73466b93cead3c6c8d3be89ce0ebe372ec9abea854cc33dee3d2
View on Chainz β†—

Height

#617,919

Difficulty

10.946595

Transactions

1

Size

207 B

Version

2

Bits

0af25413

Nonce

1,018,219,867

Timestamp

7/5/2014, 9:08:48 AM

Confirmations

6,208,668

Merkle Root

2a226b3085ad1a49bcb775d63d219e032acd3b6b739c38b61ae74c7647555f8b
Transactions (1)
Coinbase2a226b3085ad1a…e74c7647555f8b
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.348 Γ— 10⁹⁸(99-digit number)
13483399263710376351…76853113665531059200
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
1.348 Γ— 10⁹⁸(99-digit number)
13483399263710376351…76853113665531059199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.348 Γ— 10⁹⁸(99-digit number)
13483399263710376351…76853113665531059201
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
2.696 Γ— 10⁹⁸(99-digit number)
26966798527420752703…53706227331062118399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.696 Γ— 10⁹⁸(99-digit number)
26966798527420752703…53706227331062118401
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
5.393 Γ— 10⁹⁸(99-digit number)
53933597054841505406…07412454662124236799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.393 Γ— 10⁹⁸(99-digit number)
53933597054841505406…07412454662124236801
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
1.078 Γ— 10⁹⁹(100-digit number)
10786719410968301081…14824909324248473599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.078 Γ— 10⁹⁹(100-digit number)
10786719410968301081…14824909324248473601
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
2.157 Γ— 10⁹⁹(100-digit number)
21573438821936602162…29649818648496947199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.157 Γ— 10⁹⁹(100-digit number)
21573438821936602162…29649818648496947201
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 617919

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 f7c557b81a0f73466b93cead3c6c8d3be89ce0ebe372ec9abea854cc33dee3d2

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 #617,919 on Chainz β†—
Circulating Supply:57,856,847 XPMΒ·at block #6,826,586 Β· updates every 60s
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