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Block #205,971

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/12/2013, 12:14:23 PM Β· Difficulty 9.9005 Β· 6,621,343 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
14b7b2e724753f6191a42ef65cc47ed87beb7092caf2077e1176d5cad9dea37d
View on Chainz β†—

Height

#205,971

Difficulty

9.900530

Transactions

1

Size

200 B

Version

2

Bits

09e6891b

Nonce

335,568

Timestamp

10/12/2013, 12:14:23 PM

Confirmations

6,621,343

Mined by

⛏️ P2SHAbJUC2oSrZY84nuu7WUoHPgJjAcpKam6LK

Merkle Root

300865b8db2dbd29a6a0a4f5c4bcf53c9c24946fe1e67c7360e8707c0dfb2bc3
Transactions (1)
Coinbase300865b8db2dbd…e8707c0dfb2bc3
1 in β†’ 1 out10.1900 XPM109 B
AbJUC2oS…cpKam6LK
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.

6.056 Γ— 10⁹⁢(97-digit number)
60568729893881980081…23186983657054671359
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
6.056 Γ— 10⁹⁢(97-digit number)
60568729893881980081…23186983657054671359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.056 Γ— 10⁹⁢(97-digit number)
60568729893881980081…23186983657054671361
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
1.211 Γ— 10⁹⁷(98-digit number)
12113745978776396016…46373967314109342719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.211 Γ— 10⁹⁷(98-digit number)
12113745978776396016…46373967314109342721
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
2.422 Γ— 10⁹⁷(98-digit number)
24227491957552792032…92747934628218685439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.422 Γ— 10⁹⁷(98-digit number)
24227491957552792032…92747934628218685441
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
4.845 Γ— 10⁹⁷(98-digit number)
48454983915105584064…85495869256437370879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.845 Γ— 10⁹⁷(98-digit number)
48454983915105584064…85495869256437370881
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
9.690 Γ— 10⁹⁷(98-digit number)
96909967830211168129…70991738512874741759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,862,624 XPMΒ·at block #6,827,313 Β· updates every 60s
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