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Block #6,784,920

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/5/2026, 10:42:11 PM Β· Difficulty 10.9809 Β· 11,663 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
38cffa1a36b3941c96fee3532ca6eb067e0b15e8ac6d81354121c0827c20c3ce
View on Chainz β†—

Height

#6,784,920

Difficulty

10.980865

Transactions

1

Size

193 B

Version

536870912

Bits

0afb1a00

Nonce

1,082,965,316

Timestamp

4/5/2026, 10:42:11 PM

Confirmations

11,663

Mined by

⛏️ coinsforall.ioAMrLYUQNEy77yWCvavo6WLcMvQjwjifxizVisit pool β†—

Merkle Root

d20f4b1029c8a01d427d830d13c0a17a5988e8eb6f255149d0fbd7cef050870a
Transactions (1)
Coinbased20f4b1029c8a0…fbd7cef050870a
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.

1.200 Γ— 10⁹⁹(100-digit number)
12005314703814711799…78076986508898467839
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
1.200 Γ— 10⁹⁹(100-digit number)
12005314703814711799…78076986508898467839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.200 Γ— 10⁹⁹(100-digit number)
12005314703814711799…78076986508898467841
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
2.401 Γ— 10⁹⁹(100-digit number)
24010629407629423598…56153973017796935679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.401 Γ— 10⁹⁹(100-digit number)
24010629407629423598…56153973017796935681
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
4.802 Γ— 10⁹⁹(100-digit number)
48021258815258847197…12307946035593871359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.802 Γ— 10⁹⁹(100-digit number)
48021258815258847197…12307946035593871361
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
9.604 Γ— 10⁹⁹(100-digit number)
96042517630517694395…24615892071187742719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.604 Γ— 10⁹⁹(100-digit number)
96042517630517694395…24615892071187742721
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
1.920 Γ— 10¹⁰⁰(101-digit number)
19208503526103538879…49231784142375485439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.920 Γ— 10¹⁰⁰(101-digit number)
19208503526103538879…49231784142375485441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.841 Γ— 10¹⁰⁰(101-digit number)
38417007052207077758…98463568284750970879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,616,666 XPMΒ·at block #6,796,582 Β· updates every 60s
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