Block #215,625

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 5:23:16 AM · Difficulty 9.9255 · 6,577,358 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a1c16be72550115c1bee244ac88b6c00848b738385f778429d0a629d51a212e3

View on Chainz ↗

Height

#215,625

Difficulty

9.925486

Transactions

Size

3.31 KB

Version

Bits

09ececac

Nonce

51,040

Timestamp

10/18/2013, 5:23:16 AM

Confirmations

6,577,358

Merkle Root

ba5225a965313fcaac74d3c9f3244858949f0c4aa2df5861e07bed2b234496cf

Transactions (4)

Coinbase655a88161289aa…1cecf2b83fbbee

1 in → 1 out10.1900 XPM100 B

AaXb6Ldz…XefG91jF

770c9e6d633d0a…3b3ad0bf247646

13 in → 2 out370.3003 XPM1.96 KB

APbAMzL9…WTqwkJuS ARwANRKq…cKUVJex6

3cc82a3ce96a5f…2760d6b9ccf1c0

4 in → 2 out100.1200 XPM670 B

ATASjJK3…9C6dvSHc ASGVCjyE…kKyHfsac

968a3d7c4341dc…ff7a0887be0fb7

3 in → 2 out2.0308 XPM521 B

AKqxUzM4…YQ8YPmgs AHY1L1zP…op3KHdyK

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.

2.680 × 10⁹⁷(98-digit number)

26805538270533783091…12697192919598120959

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

2.680 × 10⁹⁷(98-digit number)

26805538270533783091…12697192919598120959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.680 × 10⁹⁷(98-digit number)

26805538270533783091…12697192919598120961

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

5.361 × 10⁹⁷(98-digit number)

53611076541067566182…25394385839196241919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.361 × 10⁹⁷(98-digit number)

53611076541067566182…25394385839196241921

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

1.072 × 10⁹⁸(99-digit number)

10722215308213513236…50788771678392483839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.072 × 10⁹⁸(99-digit number)

10722215308213513236…50788771678392483841

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

2.144 × 10⁹⁸(99-digit number)

21444430616427026473…01577543356784967679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.144 × 10⁹⁸(99-digit number)

21444430616427026473…01577543356784967681

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

4.288 × 10⁹⁸(99-digit number)

42888861232854052946…03155086713569935359

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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