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Block #52,015

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 8:24:39 AM Β· Difficulty 8.9066 Β· 6,753,651 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
33082c5122ac70f6c9685273eabb1a28119ea34594246e89110fc6dedf7242d9
View on Chainz β†—

Height

#52,015

Difficulty

8.906565

Transactions

1

Size

201 B

Version

2

Bits

08e814a1

Nonce

237

Timestamp

7/16/2013, 8:24:39 AM

Confirmations

6,753,651

Mined by

⛏️ P2SHAXY6feytV6ZxBQJFLAbLwdMRw9oghmWWGf

Merkle Root

91149cef5dc08801523cacc81fbfe5b5358e85dcba9ed45a1b9f15a87a0590ae
Transactions (1)
Coinbase91149cef5dc088…9f15a87a0590ae
1 in β†’ 1 out12.5900 XPM110 B
AXY6feyt…oghmWWGf
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.

1.576 Γ— 10⁹⁢(97-digit number)
15760373259358929306…22205770867540292199
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
1.576 Γ— 10⁹⁢(97-digit number)
15760373259358929306…22205770867540292199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.576 Γ— 10⁹⁢(97-digit number)
15760373259358929306…22205770867540292201
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
3.152 Γ— 10⁹⁢(97-digit number)
31520746518717858612…44411541735080584399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.152 Γ— 10⁹⁢(97-digit number)
31520746518717858612…44411541735080584401
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
6.304 Γ— 10⁹⁢(97-digit number)
63041493037435717225…88823083470161168799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.304 Γ— 10⁹⁢(97-digit number)
63041493037435717225…88823083470161168801
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
1.260 Γ— 10⁹⁷(98-digit number)
12608298607487143445…77646166940322337599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.260 Γ— 10⁹⁷(98-digit number)
12608298607487143445…77646166940322337601
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
2.521 Γ— 10⁹⁷(98-digit number)
25216597214974286890…55292333880644675199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,689,406 XPMΒ·at block #6,805,665 Β· updates every 60s
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