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Block #87,880

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/29/2013, 5:32:23 AM Β· Difficulty 9.2717 Β· 6,711,145 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e9182021e6f4365272463826194df069a260c1415266ef3d973b11066a6095b8
View on Chainz β†—

Height

#87,880

Difficulty

9.271706

Transactions

2

Size

427 B

Version

2

Bits

09458e80

Nonce

858

Timestamp

7/29/2013, 5:32:23 AM

Confirmations

6,711,145

Mined by

⛏️ P2SHAZHXXeZ7wZCgVM3wYkUjaoHoob5Mc7AKSy

Merkle Root

6efaa3565b7aec6100875250bfce08cabef41360a36fc024d80e243b3b49d5e9
Transactions (2)
Coinbasef73d6f928e2535…8e490a168edd36
1 in β†’ 1 out11.6300 XPM110 B
AZHXXeZ7…5Mc7AKSy
67504145c0bfd5…dae9d39dcd0283
1 in β†’ 2 out11.5900 XPM225 B
AH2n4CwG…tVh8TdqVAawn9XBp…AT8dv9Uf
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.

7.515 Γ— 10⁹⁹(100-digit number)
75152336316863014726…75166880550247356249
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
7.515 Γ— 10⁹⁹(100-digit number)
75152336316863014726…75166880550247356249
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.515 Γ— 10⁹⁹(100-digit number)
75152336316863014726…75166880550247356251
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
1.503 Γ— 10¹⁰⁰(101-digit number)
15030467263372602945…50333761100494712499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.503 Γ— 10¹⁰⁰(101-digit number)
15030467263372602945…50333761100494712501
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
3.006 Γ— 10¹⁰⁰(101-digit number)
30060934526745205890…00667522200989424999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.006 Γ— 10¹⁰⁰(101-digit number)
30060934526745205890…00667522200989425001
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
6.012 Γ— 10¹⁰⁰(101-digit number)
60121869053490411781…01335044401978849999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.012 Γ— 10¹⁰⁰(101-digit number)
60121869053490411781…01335044401978850001
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
1.202 Γ— 10¹⁰¹(102-digit number)
12024373810698082356…02670088803957699999
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:57,636,237 XPMΒ·at block #6,799,024 Β· updates every 60s
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