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Block #154,881

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/7/2013, 11:28:01 PM Β· Difficulty 9.8647 Β· 6,655,494 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
03a0960afce8afe603a0b248e876e5d4f76e318a8e9eee2bd64f8518ef6676af
View on Chainz β†—

Height

#154,881

Difficulty

9.864699

Transactions

1

Size

200 B

Version

2

Bits

09dd5cef

Nonce

410,609

Timestamp

9/7/2013, 11:28:01 PM

Confirmations

6,655,494

Mined by

⛏️ P2SHAGHegA75n7Ukc6hvJHVJLhohWPQFCmbWoV

Merkle Root

92cf17477646610c71e6ca3993503f6962657cc28f5786ef65ca17ea23c0c03d
Transactions (1)
Coinbase92cf1747764661…ca17ea23c0c03d
1 in β†’ 1 out10.2600 XPM109 B
AGHegA75…QFCmbWoV
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.

6.536 Γ— 10⁹⁢(97-digit number)
65366413287181897803…48506259452780155519
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
6.536 Γ— 10⁹⁢(97-digit number)
65366413287181897803…48506259452780155519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.536 Γ— 10⁹⁢(97-digit number)
65366413287181897803…48506259452780155521
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
1.307 Γ— 10⁹⁷(98-digit number)
13073282657436379560…97012518905560311039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.307 Γ— 10⁹⁷(98-digit number)
13073282657436379560…97012518905560311041
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
2.614 Γ— 10⁹⁷(98-digit number)
26146565314872759121…94025037811120622079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.614 Γ— 10⁹⁷(98-digit number)
26146565314872759121…94025037811120622081
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
5.229 Γ— 10⁹⁷(98-digit number)
52293130629745518242…88050075622241244159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.229 Γ— 10⁹⁷(98-digit number)
52293130629745518242…88050075622241244161
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
1.045 Γ— 10⁹⁸(99-digit number)
10458626125949103648…76100151244482488319
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:57,727,076 XPMΒ·at block #6,810,374 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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