Block #911,280

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2015, 11:39:27 PM · Difficulty 10.9315 · 5,883,036 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7084608dfe6e0f8334acf795914f8f31e02a8e4479823ed7d747946b33c2913b

View on Chainz ↗

Height

#911,280

Difficulty

10.931483

Transactions

Size

2.45 KB

Version

Bits

0aee75aa

Nonce

503,400,586

Timestamp

1/26/2015, 11:39:27 PM

Confirmations

5,883,036

Merkle Root

034350c4eeb8d163756f4a8a2bb8cc190dadc8a99feadbcbf3e901f9f21429d4

Transactions (2)

Coinbase944620de221d02…73525c2f2b98d8

1 in → 1 out8.3900 XPM116 B

ANSXnLY2…Sd25TjkD

c370a2110be2e9…1eeebd6857dc03

15 in → 2 out1197.5100 XPM2.25 KB

AVtgEinq…GDHjisJ7 AQ3SuyCM…AmNvneTb

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.

2.865 × 10⁹⁶(97-digit number)

28652785186013385267…43691255439157872639

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

2.865 × 10⁹⁶(97-digit number)

28652785186013385267…43691255439157872639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.865 × 10⁹⁶(97-digit number)

28652785186013385267…43691255439157872641

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

5.730 × 10⁹⁶(97-digit number)

57305570372026770534…87382510878315745279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.730 × 10⁹⁶(97-digit number)

57305570372026770534…87382510878315745281

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

1.146 × 10⁹⁷(98-digit number)

11461114074405354106…74765021756631490559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.146 × 10⁹⁷(98-digit number)

11461114074405354106…74765021756631490561

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

2.292 × 10⁹⁷(98-digit number)

22922228148810708213…49530043513262981119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.292 × 10⁹⁷(98-digit number)

22922228148810708213…49530043513262981121

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

4.584 × 10⁹⁷(98-digit number)

45844456297621416427…99060087026525962239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.584 × 10⁹⁷(98-digit number)

45844456297621416427…99060087026525962241

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