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Block #152,537

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/6/2013, 9:45:01 AM Β· Difficulty 9.8624 Β· 6,657,153 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a5e3437f1941ae24a33b8f42167d8c02a7eadb08beb25a401359b834a3032d42
View on Chainz β†—

Height

#152,537

Difficulty

9.862404

Transactions

2

Size

391 B

Version

2

Bits

09dcc687

Nonce

43,518

Timestamp

9/6/2013, 9:45:01 AM

Confirmations

6,657,153

Mined by

⛏️ P2SHAf2EkxVjKCN7hjRrZ7xZUZCQ3p4KPXQ92p

Merkle Root

347a3bfbe06f5fb97364a3d2e4c6f095bfc4d44b6fc3f6c3d27e793641b5d447
Transactions (2)
Coinbase6841ddaf2a7e83…0cba8b5db23015
1 in β†’ 1 out10.2800 XPM109 B
Af2EkxVj…4KPXQ92p
98392261054e90…288074d1ed047f
1 in β†’ 1 out72.0800 XPM193 B
AbxSykSg…BX71twYi
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.

5.522 Γ— 10⁹²(93-digit number)
55220390086289719337…38806435930834585599
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
5.522 Γ— 10⁹²(93-digit number)
55220390086289719337…38806435930834585599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.522 Γ— 10⁹²(93-digit number)
55220390086289719337…38806435930834585601
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
1.104 Γ— 10⁹³(94-digit number)
11044078017257943867…77612871861669171199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.104 Γ— 10⁹³(94-digit number)
11044078017257943867…77612871861669171201
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
2.208 Γ— 10⁹³(94-digit number)
22088156034515887735…55225743723338342399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.208 Γ— 10⁹³(94-digit number)
22088156034515887735…55225743723338342401
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
4.417 Γ— 10⁹³(94-digit number)
44176312069031775470…10451487446676684799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.417 Γ— 10⁹³(94-digit number)
44176312069031775470…10451487446676684801
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
8.835 Γ— 10⁹³(94-digit number)
88352624138063550940…20902974893353369599
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:57,721,596 XPMΒ·at block #6,809,689 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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