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Block #913,121

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/28/2015, 10:52:33 AM Β· Difficulty 10.9277 Β· 5,882,213 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
44ebc27488ad84ed3f7ad8d525e3e992f76c1a0ccec83f49cf359adcc382c4fc
View on Chainz β†—

Height

#913,121

Difficulty

10.927682

Transactions

2

Size

4.03 KB

Version

2

Bits

0aed7c95

Nonce

493,143,322

Timestamp

1/28/2015, 10:52:33 AM

Confirmations

5,882,213

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8c1c63b615e4530eb4f443a8c5b335037c6db3158237506906611b65b003867f
Transactions (2)
Coinbasee1e7449d203990…ccfe27ea0d1af6
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
26e5c90b484757…8049cd720bddb6
26 in β†’ 2 out50347.3318 XPM3.83 KB
AUwkjJNa…1wCXxF2gAeP3tEUa…LMNz2XLg
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.

2.900 Γ— 10⁹⁢(97-digit number)
29007936970635158141…08996036084304962399
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
2.900 Γ— 10⁹⁢(97-digit number)
29007936970635158141…08996036084304962399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.900 Γ— 10⁹⁢(97-digit number)
29007936970635158141…08996036084304962401
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
5.801 Γ— 10⁹⁢(97-digit number)
58015873941270316283…17992072168609924799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.801 Γ— 10⁹⁢(97-digit number)
58015873941270316283…17992072168609924801
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
1.160 Γ— 10⁹⁷(98-digit number)
11603174788254063256…35984144337219849599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.160 Γ— 10⁹⁷(98-digit number)
11603174788254063256…35984144337219849601
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
2.320 Γ— 10⁹⁷(98-digit number)
23206349576508126513…71968288674439699199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.320 Γ— 10⁹⁷(98-digit number)
23206349576508126513…71968288674439699201
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
4.641 Γ— 10⁹⁷(98-digit number)
46412699153016253027…43936577348879398399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.641 Γ— 10⁹⁷(98-digit number)
46412699153016253027…43936577348879398401
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:57,606,730 XPMΒ·at block #6,795,333 Β· updates every 60s
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