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Block #2,407,467

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/3/2017, 3:37:56 PM Β· Difficulty 10.8986 Β· 4,437,554 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e355a952b4c9a439ab7b5363604d61e9bee4f405a6361da805461bc2ed624742
View on Chainz β†—

Height

#2,407,467

Difficulty

10.898581

Transactions

2

Size

42.59 KB

Version

2

Bits

0ae6096e

Nonce

1,544,247,304

Timestamp

12/3/2017, 3:37:56 PM

Confirmations

4,437,554

Mined by

⛏️ P2SHAJB1vJW6KD9C5YdaRnfx3HZvhvyjAbZjkk

Merkle Root

1159bf5a31c0ae7bfac2c67446d19be0de504f9e43d5e134262cff11d0006e55
Transactions (2)
Coinbase44e7be09c62c37…3bc23790dc76a3
1 in β†’ 1 out8.8500 XPM110 B
AJB1vJW6…yjAbZjkk
2ad250f23f0289…16886e0ed29c04
380 in β†’ 2 out3200.5701 XPM42.39 KB
ActkSyUm…WiSsG3ygAYCyMY7Z…f5V24soB
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.

8.056 Γ— 10⁹³(94-digit number)
80563999247922817055…25788893076962471499
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
8.056 Γ— 10⁹³(94-digit number)
80563999247922817055…25788893076962471499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.056 Γ— 10⁹³(94-digit number)
80563999247922817055…25788893076962471501
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
1.611 Γ— 10⁹⁴(95-digit number)
16112799849584563411…51577786153924942999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.611 Γ— 10⁹⁴(95-digit number)
16112799849584563411…51577786153924943001
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
3.222 Γ— 10⁹⁴(95-digit number)
32225599699169126822…03155572307849885999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.222 Γ— 10⁹⁴(95-digit number)
32225599699169126822…03155572307849886001
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
6.445 Γ— 10⁹⁴(95-digit number)
64451199398338253644…06311144615699771999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.445 Γ— 10⁹⁴(95-digit number)
64451199398338253644…06311144615699772001
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
1.289 Γ— 10⁹⁡(96-digit number)
12890239879667650728…12622289231399543999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.289 Γ— 10⁹⁡(96-digit number)
12890239879667650728…12622289231399544001
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
2.578 Γ— 10⁹⁡(96-digit number)
25780479759335301457…25244578462799087999
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:58,004,592 XPMΒ·at block #6,845,020 Β· updates every 60s
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