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Block #87,832

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/29/2013, 4:46:44 AM Β· Difficulty 9.2712 Β· 6,730,129 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
96067df58a389e82c82df110a646b7d73889b20ba136ea44821c648fe4e4dd9c
View on Chainz β†—

Height

#87,832

Difficulty

9.271200

Transactions

1

Size

200 B

Version

2

Bits

09456d60

Nonce

273,937

Timestamp

7/29/2013, 4:46:44 AM

Confirmations

6,730,129

Mined by

⛏️ P2SHAeEXQxqG1a9HUoHobjrNQ1M2oHJ2q5dxWc

Merkle Root

bfb2ebc92a9a105c2c0184857d60d28046a074d10d05ab8896d261c6656ab015
Transactions (1)
Coinbasebfb2ebc92a9a10…d261c6656ab015
1 in β†’ 1 out11.6200 XPM109 B
AeEXQxqG…J2q5dxWc
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.

2.033 Γ— 10⁹⁢(97-digit number)
20334593035446753530…51586007515471301479
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
2.033 Γ— 10⁹⁢(97-digit number)
20334593035446753530…51586007515471301479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.033 Γ— 10⁹⁢(97-digit number)
20334593035446753530…51586007515471301481
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
4.066 Γ— 10⁹⁢(97-digit number)
40669186070893507060…03172015030942602959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.066 Γ— 10⁹⁢(97-digit number)
40669186070893507060…03172015030942602961
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
8.133 Γ— 10⁹⁢(97-digit number)
81338372141787014121…06344030061885205919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.133 Γ— 10⁹⁢(97-digit number)
81338372141787014121…06344030061885205921
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
1.626 Γ— 10⁹⁷(98-digit number)
16267674428357402824…12688060123770411839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.626 Γ— 10⁹⁷(98-digit number)
16267674428357402824…12688060123770411841
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
3.253 Γ— 10⁹⁷(98-digit number)
32535348856714805648…25376120247540823679
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:57,787,757 XPMΒ·at block #6,817,960 Β· updates every 60s
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