Block #308,720

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 6:07:53 AM · Difficulty 9.9946 · 6,487,229 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e2a5de96380f57243317df840eb74aef384e5838bffcb3a75a1b13c9994ebece

View on Chainz ↗

Height

#308,720

Difficulty

9.994592

Transactions

Size

6.28 KB

Version

Bits

09fe9d8f

Nonce

278,973

Timestamp

12/13/2013, 6:07:53 AM

Confirmations

6,487,229

Mined by

⛏️ aR<Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

02c5fa6651caf9803cdf299af07865a77373ea793400698fa2a910e2c2c3f000

Transactions (4)

Coinbasee2facfad39abf9…12284a8a91fe13

1 in → 30 out9.9800 XPM1.06 KB

Aac9Hjdg…P4ktypc3 ASWX42VM…XypQABkY AXWzmegk…XyxPXDLy AW1tmjeg…9NN765ML AUzoU19R…GnuoWf5o

1e651c75723baa…b49bb81f2d4548

1 in → 2 out1.0108 XPM227 B

AaFHkQgv…yJi7Zriu AWby7KFF…zEfUBKDp

eab1b7ecf948d6…9ee25ab45622b5

1 in → 2 out502.6624 XPM226 B

AUGKbsdQ…RCLMmDqo AcXKDViL…ZPivNwYp

c7bb8a2b98c14e…9a61bda06eb17d

32 in → 2 out37.1615 XPM4.69 KB

ATdBfx1Y…HyjgL4Ea AMLyKvjq…YHvAU7tD

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.

9.005 × 10⁹⁴(95-digit number)

90053563555069671414…13138863582152713239

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

9.005 × 10⁹⁴(95-digit number)

90053563555069671414…13138863582152713239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.005 × 10⁹⁴(95-digit number)

90053563555069671414…13138863582152713241

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

1.801 × 10⁹⁵(96-digit number)

18010712711013934282…26277727164305426479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.801 × 10⁹⁵(96-digit number)

18010712711013934282…26277727164305426481

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

3.602 × 10⁹⁵(96-digit number)

36021425422027868565…52555454328610852959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.602 × 10⁹⁵(96-digit number)

36021425422027868565…52555454328610852961

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

7.204 × 10⁹⁵(96-digit number)

72042850844055737131…05110908657221705919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.204 × 10⁹⁵(96-digit number)

72042850844055737131…05110908657221705921

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

1.440 × 10⁹⁶(97-digit number)

14408570168811147426…10221817314443411839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.440 × 10⁹⁶(97-digit number)

14408570168811147426…10221817314443411841

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