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Block #179,952

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/25/2013, 11:43:57 AM Β· Difficulty 9.8620 Β· 6,629,549 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
28e22dad0d8a2b7a06629eccfe27b51f63fa80a2a13d3fb16ffefb01adb5a222
View on Chainz β†—

Height

#179,952

Difficulty

9.862039

Transactions

1

Size

203 B

Version

2

Bits

09dcae92

Nonce

34,801

Timestamp

9/25/2013, 11:43:57 AM

Confirmations

6,629,549

Mined by

⛏️ P2SHAQ4KuZ2UkkCs8rHce3kHkL7Wmf1UKD59gi

Merkle Root

9ee0ae44b39eea783501ea4c0316c529e4f764ced017e1fb444be1377200e33a
Transactions (1)
Coinbase9ee0ae44b39eea…4be1377200e33a
1 in β†’ 1 out10.2700 XPM109 B
AQ4KuZ2U…1UKD59gi
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.

2.297 Γ— 10¹⁰³(104-digit number)
22976234549863457958…83309784042950046599
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
2.297 Γ— 10¹⁰³(104-digit number)
22976234549863457958…83309784042950046599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.297 Γ— 10¹⁰³(104-digit number)
22976234549863457958…83309784042950046601
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
4.595 Γ— 10¹⁰³(104-digit number)
45952469099726915916…66619568085900093199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.595 Γ— 10¹⁰³(104-digit number)
45952469099726915916…66619568085900093201
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
9.190 Γ— 10¹⁰³(104-digit number)
91904938199453831832…33239136171800186399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.190 Γ— 10¹⁰³(104-digit number)
91904938199453831832…33239136171800186401
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
1.838 Γ— 10¹⁰⁴(105-digit number)
18380987639890766366…66478272343600372799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.838 Γ— 10¹⁰⁴(105-digit number)
18380987639890766366…66478272343600372801
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
3.676 Γ— 10¹⁰⁴(105-digit number)
36761975279781532732…32956544687200745599
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:57,720,081 XPMΒ·at block #6,809,500 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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