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Block #162,416

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2013, 7:26:05 AM Β· Difficulty 9.8611 Β· 6,634,262 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
eea7597e8d6eeabf102116954d588905e6d6610ab33eee67cd99d1aa54518b41
View on Chainz β†—

Height

#162,416

Difficulty

9.861088

Transactions

1

Size

197 B

Version

2

Bits

09dc7040

Nonce

25,015

Timestamp

9/13/2013, 7:26:05 AM

Confirmations

6,634,262

Mined by

⛏️ P2SHANHdEAYnG4HaHTdmo4u2875QdotWioiVGQ

Merkle Root

af1db46fa7ce98791038059b6baab050fb5f4aeeafe94f58802f98aace18dac4
Transactions (1)
Coinbaseaf1db46fa7ce98…2f98aace18dac4
1 in β†’ 1 out10.2700 XPM109 B
ANHdEAYn…tWioiVGQ
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.

2.411 Γ— 10⁸⁹(90-digit number)
24117836009104580527…99752791432640517749
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
2.411 Γ— 10⁸⁹(90-digit number)
24117836009104580527…99752791432640517749
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.411 Γ— 10⁸⁹(90-digit number)
24117836009104580527…99752791432640517751
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
4.823 Γ— 10⁸⁹(90-digit number)
48235672018209161054…99505582865281035499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.823 Γ— 10⁸⁹(90-digit number)
48235672018209161054…99505582865281035501
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
9.647 Γ— 10⁸⁹(90-digit number)
96471344036418322109…99011165730562070999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.647 Γ— 10⁸⁹(90-digit number)
96471344036418322109…99011165730562071001
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
1.929 Γ— 10⁹⁰(91-digit number)
19294268807283664421…98022331461124141999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.929 Γ— 10⁹⁰(91-digit number)
19294268807283664421…98022331461124142001
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
3.858 Γ— 10⁹⁰(91-digit number)
38588537614567328843…96044662922248283999
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:57,617,429 XPMΒ·at block #6,796,677 Β· updates every 60s
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