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Block #1,534,746

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 10:55:48 AM Β· Difficulty 10.6180 Β· 5,273,314 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b2154ba02a77bad9d4d94582fee7f206525c56a66747ad117f45b76fac69dce7
View on Chainz β†—

Height

#1,534,746

Difficulty

10.618044

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e3823

Nonce

1,688,726,846

Timestamp

4/10/2016, 10:55:48 AM

Confirmations

5,273,314

Mined by

⛏️ P2SHAFyz7K8LxyMgEVL3yM35uCkjLS7zBzFHaZ

Merkle Root

be9d1ec889e37893983bd4bef4ad563c6896b0eae009d3426035913107b0975e
Transactions (2)
Coinbase2a461e6f466e06…277d12604fbe16
1 in β†’ 1 out8.9400 XPM109 B
AFyz7K8L…7zBzFHaZ
3312af61519dc0…2966ea0c6b8938
51 in β†’ 1 out241.2267 XPM7.41 KB
AXoixEJW…tmabgttZ
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.

9.903 Γ— 10⁹³(94-digit number)
99034708100502686134…19971872737408506119
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
9.903 Γ— 10⁹³(94-digit number)
99034708100502686134…19971872737408506119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.903 Γ— 10⁹³(94-digit number)
99034708100502686134…19971872737408506121
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
1.980 Γ— 10⁹⁴(95-digit number)
19806941620100537226…39943745474817012239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.980 Γ— 10⁹⁴(95-digit number)
19806941620100537226…39943745474817012241
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
3.961 Γ— 10⁹⁴(95-digit number)
39613883240201074453…79887490949634024479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.961 Γ— 10⁹⁴(95-digit number)
39613883240201074453…79887490949634024481
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
7.922 Γ— 10⁹⁴(95-digit number)
79227766480402148907…59774981899268048959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.922 Γ— 10⁹⁴(95-digit number)
79227766480402148907…59774981899268048961
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
1.584 Γ— 10⁹⁡(96-digit number)
15845553296080429781…19549963798536097919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.584 Γ— 10⁹⁡(96-digit number)
15845553296080429781…19549963798536097921
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
3.169 Γ— 10⁹⁡(96-digit number)
31691106592160859563…39099927597072195839
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:57,708,524 XPMΒ·at block #6,808,059 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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