Block #122,627

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/18/2013, 2:36:40 PM · Difficulty 9.7566 · 6,680,917 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a45839ca3c90d172731be2246c4199db776ae31c3352916286c59bc85b80b2c2

View on Chainz ↗

Height

#122,627

Difficulty

9.756601

Transactions

Size

396 B

Version

Bits

09c1b093

Nonce

530,519

Timestamp

8/18/2013, 2:36:40 PM

Confirmations

6,680,917

Mined by

⛏️ P2SHAFoBNhcwjYpyvYGGp3VgKQJTwgDg64LDUo

Merkle Root

2a4f6ffeba1405126a079312bb2678738c64625d45515b706a02104df9abe5c6

Transactions (2)

Coinbasea32f4ce61d49fc…9d5180ba15649a

1 in → 1 out10.5000 XPM109 B

AFoBNhcw…Dg64LDUo

2ab699920e593d…207ef7f4052767

1 in → 2 out10.5000 XPM193 B

AXUtFnVB…2K4kmJnq AYQKge85…Nkd4Hodg

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.

2.409 × 10¹⁰³(104-digit number)

24095646924144482017…05994969841048656299

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

2.409 × 10¹⁰³(104-digit number)

24095646924144482017…05994969841048656299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.409 × 10¹⁰³(104-digit number)

24095646924144482017…05994969841048656301

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

4.819 × 10¹⁰³(104-digit number)

48191293848288964035…11989939682097312599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.819 × 10¹⁰³(104-digit number)

48191293848288964035…11989939682097312601

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

9.638 × 10¹⁰³(104-digit number)

96382587696577928070…23979879364194625199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.638 × 10¹⁰³(104-digit number)

96382587696577928070…23979879364194625201

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

1.927 × 10¹⁰⁴(105-digit number)

19276517539315585614…47959758728389250399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.927 × 10¹⁰⁴(105-digit number)

19276517539315585614…47959758728389250401

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

3.855 × 10¹⁰⁴(105-digit number)

38553035078631171228…95919517456778500799

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