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Block #80,891

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/24/2013, 10:15:57 AM Β· Difficulty 9.2605 Β· 6,729,079 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
87d870ce474f04d6483513c7ddd16077cca706ef2ed8b0670120bb547c5e2854
View on Chainz β†—

Height

#80,891

Difficulty

9.260508

Transactions

1

Size

203 B

Version

2

Bits

0942b0a3

Nonce

15,152

Timestamp

7/24/2013, 10:15:57 AM

Confirmations

6,729,079

Mined by

⛏️ P2SHAGc7t72tWhbXJhPuYW3tRVfCU5UnvYxLPB

Merkle Root

15ab797c4b15070947362b993f880cdc0b554dad76966db72ce8dc7ada6130cc
Transactions (1)
Coinbase15ab797c4b1507…e8dc7ada6130cc
1 in β†’ 1 out11.6400 XPM109 B
AGc7t72t…UnvYxLPB
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.

2.420 Γ— 10¹⁰⁡(106-digit number)
24208862776457041216…93623221541516680119
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
2.420 Γ— 10¹⁰⁡(106-digit number)
24208862776457041216…93623221541516680119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.420 Γ— 10¹⁰⁡(106-digit number)
24208862776457041216…93623221541516680121
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
4.841 Γ— 10¹⁰⁡(106-digit number)
48417725552914082432…87246443083033360239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.841 Γ— 10¹⁰⁡(106-digit number)
48417725552914082432…87246443083033360241
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
9.683 Γ— 10¹⁰⁡(106-digit number)
96835451105828164864…74492886166066720479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.683 Γ— 10¹⁰⁡(106-digit number)
96835451105828164864…74492886166066720481
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
1.936 Γ— 10¹⁰⁢(107-digit number)
19367090221165632972…48985772332133440959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.936 Γ— 10¹⁰⁢(107-digit number)
19367090221165632972…48985772332133440961
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
3.873 Γ— 10¹⁰⁢(107-digit number)
38734180442331265945…97971544664266881919
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:57,723,833 XPMΒ·at block #6,809,969 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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