Block #309,887

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 7:40:53 PM · Difficulty 9.9950 · 6,499,470 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1bc1da7172c2c0ce032c12530e4af89332501dc884e48ae3b8807f43b1d6cf30

View on Chainz ↗

Height

#309,887

Difficulty

9.994993

Transactions

Size

2.10 KB

Version

Bits

09feb7df

Nonce

102,387

Timestamp

12/13/2013, 7:40:53 PM

Confirmations

6,499,470

Mined by

⛏️ aRbrAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

1a20ad55b25f94abe0348a7643c63df53a3013e8c058cbdbc235dd514efc77b8

Transactions (4)

Coinbase9cdbe17e64412b…4146fdeffbfe0e

1 in → 30 out9.9800 XPM1.06 KB

APeshfYV…3PKcKMKH Aac9Hjdg…P4ktypc3 ARcqMJhp…RVLToQ6S AYckRkCF…TgDe5VSp AZDkFhse…7U4YUDPM

063f08c6fc56e7…bcd5070f614d2b

1 in → 2 out4.4567 XPM227 B

ASVSSYee…6vzPUXxB AU5UtE4t…ZYcUGX7f

bcfc9e2e3ab9e3…05432b17b99f28

1 in → 2 out2.9310 XPM226 B

AZwyMUeE…rxMQeLU7 AMcBUE7T…zeEJzEED

74cc054f50a1ff…58d2b12cfd84ad

3 in → 2 out2.0485 XPM522 B

AGyhc9Ym…YqF23X8n ATuqDLmj…LtVnPj2U

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.253 × 10⁹⁴(95-digit number)

62536617105087180346…92786406167081145599

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

6.253 × 10⁹⁴(95-digit number)

62536617105087180346…92786406167081145599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.253 × 10⁹⁴(95-digit number)

62536617105087180346…92786406167081145601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.250 × 10⁹⁵(96-digit number)

12507323421017436069…85572812334162291199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.250 × 10⁹⁵(96-digit number)

12507323421017436069…85572812334162291201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.501 × 10⁹⁵(96-digit number)

25014646842034872138…71145624668324582399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.501 × 10⁹⁵(96-digit number)

25014646842034872138…71145624668324582401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

5.002 × 10⁹⁵(96-digit number)

50029293684069744277…42291249336649164799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.002 × 10⁹⁵(96-digit number)

50029293684069744277…42291249336649164801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.000 × 10⁹⁶(97-digit number)

10005858736813948855…84582498673298329599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.000 × 10⁹⁶(97-digit number)

10005858736813948855…84582498673298329601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #309,887

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