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Block #6,784,900

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/5/2026, 10:29:53 PM Β· Difficulty 10.9808 Β· 10,936 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f06a1feb0c77498f56ddd0f1f99cbad37bc928438335f384c9676cc25a559a2b
View on Chainz β†—

Height

#6,784,900

Difficulty

10.980838

Transactions

1

Size

191 B

Version

536870912

Bits

0afb1832

Nonce

254,396,507

Timestamp

4/5/2026, 10:29:53 PM

Confirmations

10,936

Mined by

⛏️ coinsforall.ioAMrLYUQNEy77yWCvavo6WLcMvQjwjifxizVisit pool β†—

Merkle Root

47d411aca112ca31704126f34e17f514515f69697e2589a3403c145f24ae203a
Transactions (1)
Coinbase47d411aca112ca…3c145f24ae203a
1 in β†’ 1 out8.1790 XPM101 B
AMrLYUQN…jwjifxiz
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.100 Γ— 10⁹⁴(95-digit number)
21005548962591248997…84029761772353303359
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.100 Γ— 10⁹⁴(95-digit number)
21005548962591248997…84029761772353303359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.100 Γ— 10⁹⁴(95-digit number)
21005548962591248997…84029761772353303361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.201 Γ— 10⁹⁴(95-digit number)
42011097925182497995…68059523544706606719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.201 Γ— 10⁹⁴(95-digit number)
42011097925182497995…68059523544706606721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
8.402 Γ— 10⁹⁴(95-digit number)
84022195850364995990…36119047089413213439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.402 Γ— 10⁹⁴(95-digit number)
84022195850364995990…36119047089413213441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.680 Γ— 10⁹⁡(96-digit number)
16804439170072999198…72238094178826426879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.680 Γ— 10⁹⁡(96-digit number)
16804439170072999198…72238094178826426881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.360 Γ— 10⁹⁡(96-digit number)
33608878340145998396…44476188357652853759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.360 Γ— 10⁹⁡(96-digit number)
33608878340145998396…44476188357652853761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,610,771 XPMΒ·at block #6,795,835 Β· updates every 60s
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