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Block #88,910

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/29/2013, 11:34:32 PM Β· Difficulty 9.2640 Β· 6,714,737 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
52fcf877bc08ea59806e7d072cebfdb4a728f4f80a9d69ef16a5175586c9eec2
View on Chainz β†—

Height

#88,910

Difficulty

9.264018

Transactions

1

Size

205 B

Version

2

Bits

094396b3

Nonce

87,543

Timestamp

7/29/2013, 11:34:32 PM

Confirmations

6,714,737

Mined by

⛏️ P2SHASXW8s4r1QTq8Djg6zDrh4WCnULM8vqY9U

Merkle Root

b2d1e68545bcee9e2320dfd0390fe6a04ddd8c8221135d103d2937a6812b1f8a
Transactions (1)
Coinbaseb2d1e68545bcee…2937a6812b1f8a
1 in β†’ 1 out11.6400 XPM109 B
ASXW8s4r…LM8vqY9U
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.

4.701 Γ— 10¹⁰⁸(109-digit number)
47011586020267528899…61457105211493490119
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
4.701 Γ— 10¹⁰⁸(109-digit number)
47011586020267528899…61457105211493490119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.701 Γ— 10¹⁰⁸(109-digit number)
47011586020267528899…61457105211493490121
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
9.402 Γ— 10¹⁰⁸(109-digit number)
94023172040535057798…22914210422986980239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.402 Γ— 10¹⁰⁸(109-digit number)
94023172040535057798…22914210422986980241
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
1.880 Γ— 10¹⁰⁹(110-digit number)
18804634408107011559…45828420845973960479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.880 Γ— 10¹⁰⁹(110-digit number)
18804634408107011559…45828420845973960481
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
3.760 Γ— 10¹⁰⁹(110-digit number)
37609268816214023119…91656841691947920959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.760 Γ— 10¹⁰⁹(110-digit number)
37609268816214023119…91656841691947920961
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
7.521 Γ— 10¹⁰⁹(110-digit number)
75218537632428046238…83313683383895841919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.521 Γ— 10¹⁰⁹(110-digit number)
75218537632428046238…83313683383895841921
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:57,673,209 XPMΒ·at block #6,803,646 Β· updates every 60s
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