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Block #1,095,983

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/8/2015, 10:18:49 PM Β· Difficulty 10.7501 Β· 5,714,564 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
34d4264649341c9c9783de0aa4ddc247876094533260089f2ddf239a52d35984
View on Chainz β†—

Height

#1,095,983

Difficulty

10.750090

Transactions

1

Size

200 B

Version

2

Bits

0ac005e9

Nonce

333,202,408

Timestamp

6/8/2015, 10:18:49 PM

Confirmations

5,714,564

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

2f129fed16accc8f9afb6071ce3d1dcfbba692c900ff05799bf322bcced1f1cd
Transactions (1)
Coinbase2f129fed16accc…f322bcced1f1cd
1 in β†’ 1 out8.6400 XPM109 B
ANCZAhFA…4XJ8NSvi
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.

2.096 Γ— 10⁹⁷(98-digit number)
20969022901337660698…82506212604530097919
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
2.096 Γ— 10⁹⁷(98-digit number)
20969022901337660698…82506212604530097919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.096 Γ— 10⁹⁷(98-digit number)
20969022901337660698…82506212604530097921
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
4.193 Γ— 10⁹⁷(98-digit number)
41938045802675321396…65012425209060195839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.193 Γ— 10⁹⁷(98-digit number)
41938045802675321396…65012425209060195841
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
8.387 Γ— 10⁹⁷(98-digit number)
83876091605350642793…30024850418120391679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.387 Γ— 10⁹⁷(98-digit number)
83876091605350642793…30024850418120391681
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
1.677 Γ— 10⁹⁸(99-digit number)
16775218321070128558…60049700836240783359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.677 Γ— 10⁹⁸(99-digit number)
16775218321070128558…60049700836240783361
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
3.355 Γ— 10⁹⁸(99-digit number)
33550436642140257117…20099401672481566719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.355 Γ— 10⁹⁸(99-digit number)
33550436642140257117…20099401672481566721
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:57,728,464 XPMΒ·at block #6,810,546 Β· updates every 60s
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