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Block #466,642

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/30/2014, 7:32:54 AM Β· Difficulty 10.4233 Β· 6,364,096 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2fb7ccfffd94a8f03dc27737d47fe2e22661eabf4df8e03987d004d05b565382
View on Chainz β†—

Height

#466,642

Difficulty

10.423313

Transactions

1

Size

200 B

Version

2

Bits

0a6c5e3e

Nonce

66,797

Timestamp

3/30/2014, 7:32:54 AM

Confirmations

6,364,096

Mined by

⛏️ P2SHASqdfRNpTunqNuXsxMBqCryK9KGfUbuqS8

Merkle Root

3b52b4e31c01c8833e2afed239b5a8a51b0cd1692a49d1577b163a1b8875602f
Transactions (1)
Coinbase3b52b4e31c01c8…163a1b8875602f
1 in β†’ 1 out9.1900 XPM109 B
ASqdfRNp…GfUbuqS8
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.

3.933 Γ— 10⁹⁷(98-digit number)
39334280294571919598…04944678166625966079
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
3.933 Γ— 10⁹⁷(98-digit number)
39334280294571919598…04944678166625966079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.933 Γ— 10⁹⁷(98-digit number)
39334280294571919598…04944678166625966081
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
7.866 Γ— 10⁹⁷(98-digit number)
78668560589143839196…09889356333251932159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.866 Γ— 10⁹⁷(98-digit number)
78668560589143839196…09889356333251932161
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
1.573 Γ— 10⁹⁸(99-digit number)
15733712117828767839…19778712666503864319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.573 Γ— 10⁹⁸(99-digit number)
15733712117828767839…19778712666503864321
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
3.146 Γ— 10⁹⁸(99-digit number)
31467424235657535678…39557425333007728639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.146 Γ— 10⁹⁸(99-digit number)
31467424235657535678…39557425333007728641
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
6.293 Γ— 10⁹⁸(99-digit number)
62934848471315071357…79114850666015457279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.293 Γ— 10⁹⁸(99-digit number)
62934848471315071357…79114850666015457281
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:57,890,041 XPMΒ·at block #6,830,737 Β· updates every 60s
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