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Block #457,738

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/24/2014, 3:07:26 AM Β· Difficulty 10.4184 Β· 6,337,360 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a3dd1bf3550861d04b23077bc96d635e54ee1d442e4de5907ec350eff8d14e63
View on Chainz β†—

Height

#457,738

Difficulty

10.418367

Transactions

1

Size

203 B

Version

2

Bits

0a6b1a15

Nonce

19,154

Timestamp

3/24/2014, 3:07:26 AM

Confirmations

6,337,360

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

0e74bf4082c1a7f22a17c09ab7afcacc5254bedb5b023bbb664ab0a98ad59bbc
Transactions (1)
Coinbase0e74bf4082c1a7…4ab0a98ad59bbc
1 in β†’ 1 out9.2000 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.068 Γ— 10¹⁰³(104-digit number)
10689235270906980821…31176798634004195519
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
1.068 Γ— 10¹⁰³(104-digit number)
10689235270906980821…31176798634004195519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.068 Γ— 10¹⁰³(104-digit number)
10689235270906980821…31176798634004195521
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
2.137 Γ— 10¹⁰³(104-digit number)
21378470541813961643…62353597268008391039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.137 Γ— 10¹⁰³(104-digit number)
21378470541813961643…62353597268008391041
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
4.275 Γ— 10¹⁰³(104-digit number)
42756941083627923286…24707194536016782079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.275 Γ— 10¹⁰³(104-digit number)
42756941083627923286…24707194536016782081
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
8.551 Γ— 10¹⁰³(104-digit number)
85513882167255846572…49414389072033564159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.551 Γ— 10¹⁰³(104-digit number)
85513882167255846572…49414389072033564161
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
1.710 Γ— 10¹⁰⁴(105-digit number)
17102776433451169314…98828778144067128319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.710 Γ— 10¹⁰⁴(105-digit number)
17102776433451169314…98828778144067128321
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.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,604,831 XPMΒ·at block #6,795,097 Β· updates every 60s
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