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Block #144,705

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/1/2013, 11:26:31 AM Β· Difficulty 9.8404 Β· 6,673,230 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8b741ef0c7b05255cc0b8877c1ddad9b76809edc86d76c587d5245cdafdbf447
View on Chainz β†—

Height

#144,705

Difficulty

9.840427

Transactions

3

Size

630 B

Version

2

Bits

09d72640

Nonce

211,445

Timestamp

9/1/2013, 11:26:31 AM

Confirmations

6,673,230

Mined by

⛏️ P2SHAFuzTjS8GpB9DhL8DDaY3bsPUymnguVixj

Merkle Root

919472d10e944f6824b58c27990d48650ca54a5cc2ef2eb38d3b024838ec38c3
Transactions (3)
Coinbase38d4de8953e5b8…5acbaa6344c120
1 in β†’ 1 out10.3300 XPM109 B
AFuzTjS8…mnguVixj
a76018ddb14468…e03a5928cda3db
2 in β†’ 1 out20.6600 XPM271 B
ASghs1PX…d1bLDUHV
dc28f8d672c497…4e8ed4ce9abcb0
1 in β†’ 1 out10.3100 XPM159 B
AQj5CF31…Sfv2KzXY
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.

2.652 Γ— 10⁹⁢(97-digit number)
26520614782605838247…53198442667485797729
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
2.652 Γ— 10⁹⁢(97-digit number)
26520614782605838247…53198442667485797729
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.652 Γ— 10⁹⁢(97-digit number)
26520614782605838247…53198442667485797731
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
5.304 Γ— 10⁹⁢(97-digit number)
53041229565211676494…06396885334971595459
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.304 Γ— 10⁹⁢(97-digit number)
53041229565211676494…06396885334971595461
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
1.060 Γ— 10⁹⁷(98-digit number)
10608245913042335298…12793770669943190919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.060 Γ— 10⁹⁷(98-digit number)
10608245913042335298…12793770669943190921
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
2.121 Γ— 10⁹⁷(98-digit number)
21216491826084670597…25587541339886381839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.121 Γ— 10⁹⁷(98-digit number)
21216491826084670597…25587541339886381841
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
4.243 Γ— 10⁹⁷(98-digit number)
42432983652169341195…51175082679772763679
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:57,787,545 XPMΒ·at block #6,817,934 Β· updates every 60s
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