Block #61,925

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 4:06:47 PM · Difficulty 8.9748 · 6,745,798 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e778b7935fc822b7e39b0950d55826e6853a5ce90cfe9edf760b63fb0a2aaa75

View on Chainz ↗

Height

#61,925

Difficulty

8.974791

Transactions

Size

949 B

Version

Bits

08f98be8

Nonce

174

Timestamp

7/18/2013, 4:06:47 PM

Confirmations

6,745,798

Mined by

⛏️ P2SHAKTWCvJcnAw4VWuABHqbpuVVCE7UpaeE3v

Merkle Root

a3000f3e8be6d053f89390488efff6f8f11b2e67aa20bc6b0c51b2d0fa52e954

Transactions (3)

Coinbasecfd4a60575b605…bf15957bc8baa7

1 in → 1 out12.4200 XPM110 B

AKTWCvJc…7UpaeE3v

704049d59543aa…6d8b48535fb422

3 in → 2 out1.2073 XPM523 B

AGR31hTo…huRNm9p6 AVCZK4E7…uny9XMDq

1b04efb416e660…4c64e6a986f5f5

1 in → 2 out1.1835 XPM225 B

AHfXQiwF…T33GH77f AMdf2JPw…URZXPvPS

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.

3.547 × 10⁹⁷(98-digit number)

35474807879050998802…03614242496474242249

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

3.547 × 10⁹⁷(98-digit number)

35474807879050998802…03614242496474242249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.547 × 10⁹⁷(98-digit number)

35474807879050998802…03614242496474242251

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

7.094 × 10⁹⁷(98-digit number)

70949615758101997605…07228484992948484499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.094 × 10⁹⁷(98-digit number)

70949615758101997605…07228484992948484501

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

1.418 × 10⁹⁸(99-digit number)

14189923151620399521…14456969985896968999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.418 × 10⁹⁸(99-digit number)

14189923151620399521…14456969985896969001

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

2.837 × 10⁹⁸(99-digit number)

28379846303240799042…28913939971793937999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.837 × 10⁹⁸(99-digit number)

28379846303240799042…28913939971793938001

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

5.675 × 10⁹⁸(99-digit number)

56759692606481598084…57827879943587875999

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

Block #61,925

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