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Block #240,170

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/2/2013, 12:08:57 PM Β· Difficulty 9.9558 Β· 6,566,803 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
70f030d0fc03c237a2777b8d45760111c3864cc16479d65b77b757cae22f4711
View on Chainz β†—

Height

#240,170

Difficulty

9.955754

Transactions

1

Size

201 B

Version

2

Bits

09f4ac43

Nonce

6,744

Timestamp

11/2/2013, 12:08:57 PM

Confirmations

6,566,803

Mined by

⛏️ P2SHAFv4GxfhFidL8Dd2giAFtoCmE3LfEWFx48

Merkle Root

4a4145f48d012d89bbbc9f79e650b4dc7ecacf9845049aaaf09778eb7a4c0005
Transactions (1)
Coinbase4a4145f48d012d…9778eb7a4c0005
1 in β†’ 1 out10.0700 XPM109 B
AFv4Gxfh…LfEWFx48
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.

2.229 Γ— 10⁹⁹(100-digit number)
22295876985853996203…07226351253295472639
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
2.229 Γ— 10⁹⁹(100-digit number)
22295876985853996203…07226351253295472639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.229 Γ— 10⁹⁹(100-digit number)
22295876985853996203…07226351253295472641
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
4.459 Γ— 10⁹⁹(100-digit number)
44591753971707992406…14452702506590945279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.459 Γ— 10⁹⁹(100-digit number)
44591753971707992406…14452702506590945281
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
8.918 Γ— 10⁹⁹(100-digit number)
89183507943415984813…28905405013181890559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.918 Γ— 10⁹⁹(100-digit number)
89183507943415984813…28905405013181890561
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
1.783 Γ— 10¹⁰⁰(101-digit number)
17836701588683196962…57810810026363781119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.783 Γ— 10¹⁰⁰(101-digit number)
17836701588683196962…57810810026363781121
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
3.567 Γ— 10¹⁰⁰(101-digit number)
35673403177366393925…15621620052727562239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.567 Γ— 10¹⁰⁰(101-digit number)
35673403177366393925…15621620052727562241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,699,885 XPMΒ·at block #6,806,972 Β· updates every 60s
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